We present a theory of multi‐pair excitations in strongly interacting Fermi systems. Based on an equations‐of‐motion approach for time‐dependent pair correlations it leads to a qualitatively new structure of the density‐density response function. Our theory reduces to both, i) the “correlated” random‐phase approximation (RPA) for fermions if the two‐pair excitations are ignored, and ii) the correlated Brillouin‐Wigner perturbation theory for bosons in the appropriate limit. The theory preserves the two first energy‐weighted sum rules. A familiar problem of the standard RPA is that its zero‐sound mode is energetically much higher than found in experiments. The popular cure of introducing an average effective mass in the Lindhard function violates sum rules and describes the physics incorrectly. We demonstrate that the inclusion of correlated pair excitations gives the correct dispersion. As in 4He, a modification of the effective mass is unnecessary also in 3He.We present a theory of multi‐pair excitations in strongly interacting Fermi systems. Based on an equations‐of‐motion approach for time‐dependent pair correlations it leads to a qualitatively new structure of the density‐density response function. Our theory reduces to both, i) the “correlated” random‐phase approximation (RPA) for fermions if the two‐pair excitations are ignored, and ii) the correlated Brillouin‐Wigner perturbation theory for bosons in the appropriate limit. The theory preserves the two first energy‐weighted sum rules. A familiar problem of the standard RPA is that its zero‐sound mode is energetically much higher than found in experiments. The popular cure of introducing an average effective mass in the Lindhard function violates sum rules and describes the physics incorrectly. We demonstrate that the inclusion of correlated pair excitations gives the correct dispersion. As in 4He, a modification of the effective mass is unnecessary also in 3He.

AIP conference proceedingsJan 1, 20061 citation

Theory of many-boson systems

Richard David Etters

Jan 1, 19650 citations

Theory of many-boson systems

Richard David Etters

Jan 1, 19650 citations

Number-conserving model for boson pairing

Stefano Fantoni, T. M. Nguyen, Subodh R. Shenoy +1 more

An independent-pair ansatz is developed for the many-body wave function of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full Hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic-energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two-body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction, and (vi) the pairing function, which quantifies the off-diagonal long-range order resulting from the structural properties of the two-particle density matrix. The connections with the low-density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atom Bose-Einstein condensates. Comparison with the available diffusion Monte Carlo results is also made.An independent-pair ansatz is developed for the many-body wave function of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full Hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic-energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two-body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction, and (vi) the pairing function, which quantifies the off-diagonal long-range order resulting from the structural properties of the two-particle density matrix. The connections with the low-density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atom Bose-Einstein condensates. Comparison with the available diffusion Monte Carlo results is also made.

arXiv:cond-mat/0205282Physical Review ASep 11, 20026 citations

Theory of many-boson systems in the weak coupling limit

D.K. Lee

Physics Letters AOct 1, 19715 citations

Sum-rules for Raman scattering off strongly correlated electron systems

Luca de’ Medici, Antoine Georges, Gabriel Kotliar

We investigate sum-rules applying to the Raman intensity in a strongly correlated system close to the Mott transition. Quite generally, it can be shown that provided the frequency integration is performed up to a cutoff smaller than the upper Hubbard band a sum-rule applies to the nonresonant Raman signal of a doped Mott insulator, resulting in an integrated intensity, which is proportional to the doping level. We provide a detailed derivation of this sum-rule for the $t\text{\ensuremath{-}}J$ model for which the frequency cutoff can be taken to infinity and an unrestricted sum-rule applies. A quantitative analysis of the sum-rule is also presented for the $d$ -wave superconducting phase of the $t\text{\ensuremath{-}}J$ model, using slave-boson methods. The case of the Hubbard model is studied in the framework of dynamical mean-field theory, with special attention to the cut-off dependence of the restricted sum-rule and also to the intermediate coupling regime. The sum-rule investigated here is shown to be consistent with recent experimental data on cuprate superconductors, reporting measurements of Raman scattering intensities on an absolute scale.We investigate sum-rules applying to the Raman intensity in a strongly correlated system close to the Mott transition. Quite generally, it can be shown that provided the frequency integration is performed up to a cutoff smaller than the upper Hubbard band a sum-rule applies to the nonresonant Raman signal of a doped Mott insulator, resulting in an integrated intensity, which is proportional to the doping level. We provide a detailed derivation of this sum-rule for the $t\text{\ensuremath{-}}J$ model for which the frequency cutoff can be taken to infinity and an unrestricted sum-rule applies. A quantitative analysis of the sum-rule is also presented for the $d$-wave superconducting phase of the $t\text{\ensuremath{-}}J$ model, using slave-boson methods. The case of the Hubbard model is studied in the framework of dynamical mean-field theory, with special attention to the cut-off dependence of the restricted sum-rule and also to the intermediate coupling regime. The sum-rule investigated here is shown to be consistent with recent experimental data on cuprate superconductors, reporting measurements of Raman scattering intensities on an absolute scale.

arXiv:0803.0752Physical Review BJun 23, 200810 citations

d

-wave superconducting phase of the $t\text{\ensuremath{-}}J$ model, using slave-boson methods. The case of the Hubbard model is studied in the framework of dynamical mean-field theory, with special attention to the cut-off dependence of the restricted sum-rule and also to the intermediate coupling regime. The sum-rule investigated here is shown to be consistent with recent experimental data on cuprate superconductors, reporting measurements of Raman scattering intensities on an absolute scale.